P(P1) =1 .....as can be placed anywhere in the circle. .......................... ref pic 01

p(P2)= 120/360=1/3 as........ p2 can be at max r(radius) dist from p1. thus forms equilateral trangle at both sides when reference OP1. Thus max possible placement is at 1/3 of 360 deg

..............ref pic 02

For P3 only 2 cases:

case 01 : p1 & p2 at same pt thus p3 at r dist , hence fracton again covers 120 deg out of 360 . Hence p3= 120/360=1/3 ...........ref pic 03

case 02 : when p1 & p2 are not at the same point , then the max arc covered by 2 max distant points is 60. p3=60/360 =1/6 ................ref pic 04

P(P1 P2 P3case01)= 1*1/3*1/3 =1/9

P(P1 P2 P3case01)= 1*1/3*1/6 =1/18........ as these are the 2 extreme cases the actual P is in between.

..................Thus Ans is B.

Attachments

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Please let me know if I am going in wrong direction.

Thanks in appreciation.